"Both ordered logistic and probit regression are very similar to each other. It can be used when the respose variable is ordered / ranked."

Ordered Probit / Logit regression can be implemented using the polr() function in MASS package. Some examples of ordered response variable could be ‘size’, ‘ranks’, ‘ratings’ etc.

library (MASS)
orderedLogitModel <- polr (orderedResponse ~ pred1 + pred2 + pred3, data=inputData, Hess=TRUE) # ordered logit
summary (orderedLogitModel) # view a summary of the model
orderedProbitModel <- polr (orderedResponse ~ pred1 + pred2 + pred3, data=inputData, method="probit") # ordered probit
predict (orderedLogitModel, newData, type = "p") # predict on new data